1. If the measures of the sides of triangle are $$(x ^{2} - 1), (x^{2} + 1)$$ and 2x cm, then the triangle would be
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By: anil on 05 May 2019 01.52 am
Sides of the triangle are = $$(x ^{2} - 1), (x^{2} + 1)$$ and $$2x$$ By putting $$x$$ = 2, we get the sides as 3,4,5 which are the sides of right angled triangle.Thus, we need to check for only right angled triangle Clearly, longest side here is $$(x^2+1)$$
=> $$[(x^2-1)^2 + (2x)^2]$$ = $$(x^4 + 1 - 2x^2 + 4x^2)$$ = $$(x^4 + 2x^2 + 1)$$ = $$(x^2 + 1)^2$$ Thus, these are the sides of a right angled triangle.
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=> $$[(x^2-1)^2 + (2x)^2]$$ = $$(x^4 + 1 - 2x^2 + 4x^2)$$ = $$(x^4 + 2x^2 + 1)$$ = $$(x^2 + 1)^2$$ Thus, these are the sides of a right angled triangle.